= Counterpropagating-pump phase matching
{title2=$\mathbf k_1+\mathbf k_2=0$}
For opposite equal pump <wave vectors>, a conjugate mixing source has <wave vector> $-\mathbf k_3$. In an isotropic nondispersive medium this exactly matches a free backward wave at the generated <frequency> only in the degenerate case. Away from degeneracy the longitudinal mismatch has magnitude $2n|\omega_P-\omega_3|/c$; a finite interaction length supplies a tolerance, not exact vector matching.
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